Name _______________
Date ____________
Period _____________
Notes 5-7: Pythagorean Theorem
Objectives: 1. Use the Pythagorean theorem and its converse to solve problems.
2. Use Pythagorean inequalities to classify triangles.
Legs: _____ & _____
c
a
Hypotenuse: _____
b
Pythagorean Theorem: In a right triangle, the________ of the squares of the
______________ of the legs equals the ______________ of the length of the hypotenuse.
a2 + b2 = _____
1)
2)
x
x
6
3
8
4
3)
4)
x
12
x
3
11
7
5)
6)
90
x
10
26
10
x
x+2
7)
8)
9) Find the length of the diagonal of a square with perimeter 12.
Pythagorean Triples
____, ____, ____
____, ____, ____
____, ____, ____
____, ____, ____
Find the missing side and tell if the side lengths form a Pythagorean Triple.
10)
11)
12)
13)
Converse of the Pythagorean Theorem: If the square of one side of a triangle is equal to the
______ of the ______________ of the other two sides, then the triangle is a _________
triangle.
Decide if the following lengths can form a right triangle.
14)
6, 8, 10
______
15)
10, 24, 26
______
16)
9, 12, 18
______
17)
16, 30, 34
______
Pythagorean Inequalities Theorem:
If c2 = a2 + b2, then mC ____ 90, and ΔABC is __________.
If c2 > a2 + b2, then mC ____ 90, and ΔABC is __________.
If c2 < a2 + b2, then mC ____ 90, and ΔABC is __________.
Decide if the following triangles are right, obtuse, or acute.
18)
9, 40, 41
19)
6, 7, 8
20)
7, 8, 11